I agree with your determinant. Can you post the rest of your working?
There are 2 ways taught us to solve for this using matrix.
The Inverse method and Row-Echelon method.
In row echelon method i got this answer:
i know the answer is correct because when i substitute it to the equations above, i get the correct answer.
My problem is, when I use the Inverse method, i get the determinant -18, and the rest of the process gives me a wrong answer.